Generalized skew polynomial rings
HTML articles powered by AMS MathViewer
- by John Dauns
- Trans. Amer. Math. Soc. 271 (1982), 575-586
- DOI: https://doi.org/10.1090/S0002-9947-1982-0654851-2
- PDF | Request permission
Abstract:
For a totally ordered cancellative semigroup $\Gamma$, a skew field $K$, let $K[\Gamma ;\phi ]$ be a skew semigroup ring. If $x \in \Gamma , k \in K$, then $kx = x{k^x}$, where $k \to {k^x}$ is an endomorphism of $K$ depending on $x$. Ideals of $K[\Gamma ;\phi ]$ are investigated for various semigroups or groups $\Gamma$.References
- P. M. Cohn, Free rings and their relations, London Mathematical Society Monographs, No. 2, Academic Press, London-New York, 1971. MR 0371938
- Paul Moritz Cohn, Skew field constructions, London Mathematical Society Lecture Note Series, No. 27, Cambridge University Press, Cambridge-New York-Melbourne, 1977. MR 0463237
- Paul Conrad, Ordered semigroups, Nagoya Math. J. 16 (1960), 51–64. MR 109850
- Paul Conrad and John Dauns, An embedding theorem for lattice-ordered fields, Pacific J. Math. 30 (1969), 385–398. MR 246859
- Paul Conrad and Paul McCarthy, The structure of $f$-algebras, Math. Nachr. 58 (1973), 169–191. MR 330000, DOI 10.1002/mana.19730580111
- John Dauns, Integral domains that are not embeddable in division rings, Pacific J. Math. 34 (1970), 27–31. MR 279018
- John Dauns, Power series semigroup rings, Pacific J. Math. 34 (1970), 365–369. MR 269569
- John Dauns, Embeddings in division rings, Trans. Amer. Math. Soc. 150 (1970), 287–299. MR 262291, DOI 10.1090/S0002-9947-1970-0262291-5
- John Dauns, Ordered domains, Symposia Mathematica, Vol. XXI (Convegno sulle Misure su Gruppi e su Spazi Vettoriali, Convegno sui Gruppi e Anelli Ordinati, INDAM, Rome, 1975), Academic Press, London, 1977, pp. 565–587. MR 0485619 —, Noncyclic division rings, Math. Z. 169 (1979), 195-204.
- John Dauns, Generalized semigroup rings, Algebra, Carbondale 1980 (Proc. Conf., Southern Illinois Univ., Carbondale, Ill., 1980) Lecture Notes in Math., vol. 848, Springer, Berlin, 1981, pp. 235–254. MR 613190
- L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864 —, Teilweise geordnete algebraische Strukturen, Akad. Kiado, Budapest, 1966.
- Charles Holland, A totally ordered integral domain with a convex left ideal which is not an ideal, Proc. Amer. Math. Soc. 11 (1960), 703. MR 125140, DOI 10.1090/S0002-9939-1960-0125140-0
- Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601
- Arun Vinayak Jategaonkar, Left principal ideal domains, J. Algebra 8 (1968), 148–155. MR 218387, DOI 10.1016/0021-8693(68)90040-9
- A. I. Mal′cev, On the embedding of group algebras in division algebras, Doklady Akad. Nauk SSSR (N.S.) 60 (1948), 1499–1501 (Russian). MR 0025457
- Susan Montgomery and D. S. Passman, Crossed products over prime rings, Israel J. Math. 31 (1978), no. 3-4, 224–256. MR 516150, DOI 10.1007/BF02761494
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
- Wayne B. Powell, Projectives in a class of lattice ordered modules, Algebra Universalis 13 (1981), no. 1, 24–40. MR 631407, DOI 10.1007/BF02483820
- M. Satyanarayana, Principal right ideal semigroups, J. London Math. Soc. (2) 3 (1971), 549–553. MR 283115, DOI 10.1112/jlms/s2-3.3.549
- Stuart A. Steinberg, An embedding theorem for commutative lattice-ordered domains, Proc. Amer. Math. Soc. 31 (1972), 409–416. MR 285464, DOI 10.1090/S0002-9939-1972-0285464-1
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 271 (1982), 575-586
- MSC: Primary 16A05; Secondary 16A02
- DOI: https://doi.org/10.1090/S0002-9947-1982-0654851-2
- MathSciNet review: 654851